Level 4: Inference · Problem 64 of 87

Bonferroni: how many tests survive

A statistics problem from Statisticsdrill. Solve it with one answer box, with a fresh sample on every attempt and the worked steps and spreadsheet function in the answer, and it is checked the moment you submit.

The task

An analyst ran 6 independent hypothesis tests, one for each of 6 product features compared between returning and new customers, and got these p-values: 0.0035, 0.029, 0.0349, 0.0185, 0.0038, 0.0031. To hold the family-wise error rate at α = 0.05, the Bonferroni correction is applied. How many of the tests are significant after the correction? Give a whole number.

What this problem teaches

The formula: Adjusted threshold = α / m. Running m tests at α each inflates the chance of at least one false positive. Dividing α by m caps that family-wise rate at α, at the cost of power. The equivalent view is to multiply each p-value by m and compare with α.

A hint if you get stuck

Bonferroni compares each p-value with α / m, where m is the number of tests. Count the p-values at or below that threshold.